334 



were originally a solid sphere, composed of concentric spheri- 

 cal strata of equal density, and covered with the water which 

 now constitutes its seas and oceans, it is evident that its rota- 

 tion would tend to give a spheroidal form to the surface of the 

 fluid. If, by the action of causes at the surface of the earth, 

 the solid sphere became gradually an oblate spheroid, the 

 direction of the resultant of the forces acting on a particle of 

 the fluid at its surface would be also gradually changed, and 

 consequently the form of the surface. The distribution of the 

 water on the earth's surface might thus be so altered as to 

 tend in some regions to lay bare the former bed of the ocean, 

 and in others to submerge the dry land. The following in- 

 vestigation shows that such a tendency would exist, and, 

 moreover, that it would be such as to establish the truth of 

 the proposition stated in the foregoing introductory remarks. 



" 2. As the causes by which the surface of the earth may 

 have acquired a spheroidal form are assumed to act only at its 

 surface, it follows that, except in the immediate vicinity of 

 that surface, its constitution must remain unchanged. It will, 

 therefore, consist of a sphere composed of concentric spherical 

 strata surrounded by a solid mass, having its mean density 

 equal to that of the surface stratum of the sphere, and in- 

 cluded between a spherical and spheroidal surface, together 

 with the fluid mass covering the latter. The surface of the 

 fluid being spheroidal, and the surface bounding the exterior 

 solid mass having necessarily a small ellipticity, we may sup- 

 pose that of the former surface small. In the succeeding inves- 

 tigation the second powers of these ellipticities shall therefore 

 be neglected. 



" The forces acting on a particle at the surface of the fluid 

 in equilibrium are : 



" ( 1 .) Attraction of the solid sphere with the radius a% and 

 mean density Z). 



" (2.) Attraction of the superficial mass with the density 

 Z)], bounded inwardly by the spherical surface with the radius 



